On the table, it's shown the warlock acquires new spell slots as it levels up, for example, starts at level 1 with 1 1st level slot, and then on level 2 it gets 2 1st level slots; however at level 3 it says it still has 2 slots, but now are 2nd level. Does this means he gets 2 2nd level slots? Or the 1st level slots are lost and he has vey limited slot uses of 2nd level?

1 Answer
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All warlock spell slots are the same level (PHB p.107, under the Spell Slots section). As they level, warlocks eventually reach their maximum of 4 spell slots, and their maximum spell slot level of 5.

Do note that you can cast lower level spells in slots that are higher level than the base spell (I.E., Hold Person, a second level spell, can be cast with any spell slot of level 2 or higher), and many spells specify additional effects when you cast them at higher level. In addition, the reason for the relatively limited number of slots is that unlike most casters, warlocks regain their spell slots on a short rest as well as a long rest.